2025/05/26 by Claudio Dappiaggi, Vincenzo Morinelli, Dappiaggi, Claudio +5
Mathematics · Physics and Astronomy · #81P45 #81T05 #81T20 #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2505.20191
openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a four-dimensional globally hyperbolic spacetime (M,g) conformal to Minkowski spacetime, together with a massless, conformally coupled scalar field. Using a bulk-to-boundary correspondence, one can establish the existence of an injective *-homomorphism ΥM between W(M), the Weyl algebra of observables on M and a counterpart which is defined intrinsically on future null infinity \Im+≃ℝ×\mathbbS2, a component of the conformal boundary of (M,g). Using invariance under the asymptotic symmetry group of \Im+, we can individuate thereon a distinguished two-point correlation function whose pull-back to M via ΥM identifies a quasi-free Hadamard state for the bulk algebra of observables. In this setting, if we consider V+x, a future light cone stemming from x∈ M as well as W(V+x)=W(M)|V+x, its counterpart at the boundary is the Weyl subalgebra generated by suitable functions localized in Kx, a positive half strip on \Im+. To each such cone, we associate a standard subspace of the boundary one-particle Hilbert space, which coincides with the one associated naturally to Kx. We extend such correspondence replacing Kx and V+x with deformed counterparts, denoted by SC and VC. In addition, since the one particle Hilbert space at the boundary decomposes as a direct integral on the sphere of U(1)-currents defined on the real line, we prove that also the generator of the modular group associated to the standard subspace of VC decomposes as a suitable direct integral. This result allows us to study the relative entropy between coherent states of the algebras associated to the deformed cones VC establishing the quantum null energy condition.